There are, of course, lots of English-language schools in London, and probably the best known is International House. Another good one is St George's International. "Cheap" and "good" don't generally apply to the same school, you will find. A good school will have good facilities and pay good staff.
Edited to say that perhaps the schools outside the central London area are a little cheaper, and I can recommend the Golders Green College at 11 Golders Green Road. It rather depends on where you will be staying, of course, because you don't want to spend a lot of time and money on travel.